## Introduction to 2-spinors in General RelativityThis book deals with 2-spinors in general relativity, beginning by developing spinors in a geometrical way rather than using representation theory, which can be a little abstract. This gives the reader greater physical intuition into the way in which spinors behave. The book concentrates on the algebra and calculus of spinors connected with curved space-time. Many of the well-known tensor fields in general relativity are shown to have spinor counterparts. An analysis of the Lanczos spinor concludes the book, and some of the techniques so far encountered are applied to this. Exercises play an important role throughout and are given at the end of each chapter. Sample Chapter(s). Spinor Geometry (238 KB). Contents: Spinor Geometry; Spinor Algebra; Spinor Analysis; Lanczos Spinor. Readership: Postgraduate level students and researchers. |

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### Contents

Spinor geometry | 1 |

Spinor algebra | 13 |

Spinor analysis | 39 |

Lanc2os spinor | 91 |

Appendix A Aspects of general relativity | 127 |

181 | |

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### Common terms and phrases

2ero algebraically arbitrary Bianchi identities Cabcd called Christoffel symbols coefficients transform commutation complex conjugate consider constant contraction coordinate system covariant derivative covariant vector curve denoted differential operators dyad Einstein expression field equations follows geodesic geodesic coordinate system geometry given gravitational field Habc HABCC Hence independent components indices intrinsic derivatives Lanc2os coefficients Lanc2os tensor linear matrix metric tensor Minkowski space natural basis Newtonian null cone null tetrad null tetrad transforms null tetrad vectors null vectors obtained parameter partial derivatives particle Penrose Petrov type principal null directions Rabcd Ricci tensor Riemann tensor scalar field scalar quantity skew-symmetric spin basis transforms spin coefficients spin-vector spinor equivalent symmetric symmetry properties tensor equation tensor field tensor g theorem theory timelike vector Tpo(M transformation law Transvecting unique tensor univalent spinor VABCD valence vector field vector space Weyl spinor Weyl tensor Weyl-Lanc2os equations world-tensor write XABCD yields